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Benjamin J. Fregly1

Department of Mechanical and AerospaceEngineering,

University of Florida,Gainesville, FL 32611-6250;

Department of Biomedical Engineering,University of Florida,

Gainesville, FL 32611-6131;and Department of Orthopaedics and

Rehabilitation,University of Florida,

Gainesville, FL 32611-2727e-mail: fregly@ufl.edu

Carlos Marquez-BarrientosDepartment of Biomedical Engineering,

University of Florida,Gainesville, FL 32611-6131

Scott A. BanksDepartment of Mechanical and Aerospace

Engineering,University of Florida,

Gainesville, FL 32611-6250;Department of Biomedical Engineering,

University of Florida,Gainesville, FL 32611-6131;

and Department of Orthopaedics andRehabilitation,

University of Florida,Gainesville, FL 32611-2727

John D. DesJardinsDepartment of Bioengineering,

Clemson University,Clemson, SC 29634-0905

Increased Conformity OffersDiminishing Returns for ReducingTotal Knee Replacement WearWear remains a significant problem limiting the lifespan of total knee replacements(TKRs). Though increased conformity between TKR components has the potential todecrease wear, the optimal amount and planes of conformity have not been investigated.Furthermore, differing conformities in the medial and lateral compartments may providedesigners the opportunity to address both wear and kinematic design goals simulta-neously. This study used a computational model of a Stanmore knee simulator machineand a previously validated wear model to investigate this issue for simulated gait. TKRgeometries with different amounts and planes of conformity on the medial and lateralsides were created and tested in two phases. The first phase utilized a wide range ofsagittal and coronal conformity combinations to blanket a physically realistic designspace. The second phase performed a focused investigation of the conformity conditionsfrom the first phase to which predicted wear volume was sensitive. For the first phase,sagittal but not coronal conformity was found to have a significant effect on predictedwear volume. For the second phase, increased sagittal conformity was found to decreasepredicted wear volume in a nonlinear fashion, with reductions gradually diminishing asconformity increased. These results suggest that TKR geometric design efforts aimed atminimizing wear should focus on sagittal rather than coronal conformity and that at leastmoderate sagittal conformity is desirable in both compartments.�DOI: 10.1115/1.4000868�

Keywords: total knee arthroplasty, biomechanics, wear simulation

Introduction

Polyethylene wear remains an important factor limiting the lon-evity of total knee replacements �TKRs� �1–3�. Wear particlesiberated from the polyethylene tibial insert can induce osteolysisi.e., bone resorption caused by upregulation of osteoclast activity4,5�� which in turn can lead to component loosening �6�. ThoughKR survivorship has been reported to be 78% at 15 years �7�,

mproved wear performance is becoming increasingly importants younger, more active patients are implanted �8�. Ideally, themplant should outlive the patient while not limiting function.KR damage and survivorship have been reported to be worse inounger than in older patients �9�, causing many younger patientso limit the physical activities in which they participate.

Increased conformity between the femoral component and tibialnsert has been proposed as a means for reducing wear �1,10–13�.ncreased conformity in well-aligned implants reduces contacttresses on the polyethylene tibial insert �14–16�. These contacttress reductions are believed to result in reduced polyethyleneear �13�, since adhesive and abrasive wear is due to the com-

1Corresponding author. Present address: Department of Mechanical and Aero-pace Engineering, University of Florida, 231 MAE-A Building, P.O. Box 116250,ainesville, FL 32611-6250.

Contributed by the Bioengineering Division of ASME for publication in the JOUR-

AL OF BIOMECHANICAL ENGINEERING. Manuscript received September 24, 2008; finalanuscript received October 1, 2009; accepted manuscript posted December 21,

009; published online January 29, 2010. Assoc. Editor: Mohamed Samir Hefzy.

ournal of Biomechanical Engineering Copyright © 20

bined effect of contact stress and sliding conditions. As a sidebenefit, increased conformity has also been reported to improvethe stability of the implant �17�. However, other studies have re-ported that increased conformity may have little effect on poly-ethylene wear volume �18,19�, possibly because the decrease incontact stress is counteracted by an increase in contact area sub-jected to sliding. Furthermore, increased conformity has potentialdisadvantages such as increased contact stress if the componentsare malaligned �20–22�, increased wear due to easier entrapmentof wear particles between the articular surfaces �16�, and in-creased component interface stresses �12,13,23�. Thus, one of thechallenges of TKR design is to determine the conformity condi-tions that strike a balance between these potential advantages anddisadvantages.

Testing of TKR designs with different amounts of conformityhas historically been performed using knee simulator machines,such as the Stanmore and AMTI machines as well as customdesigned machines �24–27�. Such tests are useful for screeningnew TKR designs and comparing the wear performance of differ-ent designs. However, testing of a single design typically coststens of thousands of dollars and requires several months to com-plete. Furthermore, for any particular design, variability of motionand load inputs as well as positioning of the components in themachine can have a significant influence on the resulting wearvolume �28�. These factors make it difficult to compare wear per-

formance for different TKR designs, and no studies can be found

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n the literature where head-to-head wear evaluation of a largeumber of design variations has been performed experimentally.

For these reasons, recent studies have sought to develop com-utational models of knee simulator machines to speed up andmprove the implant design process �29–33�. Such models are ableo generate wear predictions in a matter of minutes or hours forew TKR designs, rather than months as with physical wear test-ng. Recent studies have investigated whether the wear depths,reas, and volumes predicted by such models are accurate whenompared with experimental wear results obtained from the samemplant design subjected to the same motion and load inputs.hese studies have revealed that a sequence of wear simulations,here the tibial insert geometry is worn progressively from one

imulation to the next, is required to predict wear depths and areasccurately, whereas a single simulation performed with “virgin”nsert geometry is capable of predicting wear volume accurately29,31�. Computational models can therefore provide a cost effec-ive, time efficient, and well controlled complement to physicalear testing for evaluating how TKR geometry alternations �e.g.,

hanges in conformity� affect resulting wear performance. In par-icular, computational models can make it possible to evaluateystematically a wide range of geometric designs to identify theeometric parameters to which wear volume is most sensitive.

This study used a validated computational model to assess theffect of varying TKR conformity on polyethylene wear volume29,34�. The three-dimensional computational model, which mim-cked a Stanmore knee simulator machine performing a simulatedait motion, was used to perform wear simulations in two phases.he first phase blanketed a wide range of TKR conformity condi-

ions, while the second phase performed a more focused investi-ation of the conditions to which wear volume was sensitive. Usef a computational rather than experimental approach facilitatedapid evaluation of this large range of geometric designs. Theypothesis tested was that wear volume would decrease nonlin-arly with increased sagittal but not coronal conformity due to aorresponding nonlinear reduction in sliding motion. The resultsrovide general design guidelines for when increased sagittal andoronal conformity may, and may not, be valuable for reducingear volume in total knee replacements.

Methods

2.1 Stanmore Simulator Machine Model. A computationalodel of a Stanmore knee simulator machine was constructed in

he Pro/MECHANICA MOTION �Parametric Technology Corpo-ation, Waltham, MA� multibody dynamics simulation environ-ent �Fig. 1�. The tibial component in the model was allowed to

ranslate freely in the medial-lateral �ML� and anterior-posteriorAP� direction and was allowed to rotate freely around a superior-nferior �SI� axis. The femoral component was allowed to translatereely in the SI direction and rotate freely around an AP axis.hese degrees of freedom were the same as in the real simulatorachine except for two minor modifications. In the actual ma-

hine, SI translation is accommodated on the tibial rather than theemoral side, and tibial translations are achieved via sagittal andoronal plane rotations about a point far below the tibial compo-ent rather than via transverse plane translations. Other studiesave used the same modeling idealizations used here to developomputational simulations of the Stanmore machine �17,35�.

One-cycle dynamic gait simulations were performed with theomputational model using International Standards OrganizationISO� standard motion and load inputs for the Stanmore machineISO 14243-1, 2000�. An AP control force and internal-externalIE� control torque �i.e., directed about an SI axis� were applied tohe tibial component, while an SI control force was applied to theemoral component. Flexion of the femoral component was pre-cribed about the femoral flexion axis. Soft tissue restraints wereimulated by attaching two spring bumpers to the anterior and

osterior sides of the tibial component. The springs were attached

21007-2 / Vol. 132, FEBRUARY 2010

at the same locations as in the actual simulator machine, and thestiffness of each bidirectional spring was set to 14.48 N/mm for aneffective stiffness of 28.96 N/mm �24�.

Contact pressures between the femoral component and tibialinsert were calculated using a custom elastic foundation modelincorporated into the Pro/MECHANICA MOTION simulator ma-chine model �36,37�. Geometry evaluations required by the modelwere performed using the ACIS 3D Toolkit �Spatial Corporation,Westminster, CO�. To prevent excessive interpenetration, the con-tact model utilized springs distributed uniformly over the articu-lating surfaces of the tibial insert, where each spring was treatedas independent from its neighbors and was associated with asingle tibial surface element of known area. The contact pressurep for each element was calculated from �38,39�

p =�1 − ��E

�1 + ���1 − 2��d

h�1�

where E is Young’s modulus of the elastic layer �463 MPa �14��,� is the Poisson’s ratio of the elastic layer �0.45 �40��, h is thelayer thickness at the element location �average value of 10 mmacross the insert�, and d is the element’s spring deflection, definedas the interpenetration of the undeformed surfaces in the directionof the local surface normal. The distance d for each element wascomputed at each time instant from the relative position and ori-entation of the femoral component with respect to the tibial insert.Individual element pressures were converted into element forcesusing the known area of each element, and these forces weretreated as equal and opposite loads applied to the articulating sur-faces during a dynamic simulation.

Wear volume for each dynamic gait simulation was calculatedusing the predicted time histories of contact pressures and slidingconditions for each tibial insert surface element �Fig. 2�. Over thecourse of a one-cycle simulation, the total depth of material re-moved from an element �Wear was predicted using Archard’s clas-sic law for mild wear �41�

�Wear = k�i=1

n

pi�vi��ti �2�

where k is the material wear rate �representative value of1�10−7 mm3 /N m �42–45��, i is a discrete time frame within theone-cycle simulation, n is the total number of time frames, pi isthe element contact pressure at instant i, �vi� is the magnitude ofthe element’s relative sliding velocity at instant i, and �ti is the

0 20 40 60 80 100Gait cycle (percent)

Fig. 1 Computational model of a Stanmore knee simulator ma-chine constructed in Pro/MECHANICA MOTION showing ideal-ized femoral and tibial articular geometry from one of the tests.Multiple time frames over the gait cycle are displayed to illus-trate the predicted motion of the components during a dynamicsimulation.

time increment used in the analysis �34�. Wear volume for each

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urface element was calculated by multiplying element wear depthy element area, and total wear volume was calculated by sum-ing element wear volumes over all surface elements. One-cycleear volume was extrapolated out to 5�106 cycles, representa-

ive of the total number of cycles commonly used for testing in aimulator machine.

2.2 Computational Wear Tests. Computational wear testingas performed in two phases using tibial and femoral geometries

epresenting a wide range of sagittal and coronal conformities. Alleometries were created using SolidWorks computer-aided designoftware �SolidWorks Corporation, Concord, MA�. Idealizedemoral component geometry was constructed using a sagittal pro-le with three distinct radii and a coronal profile with a singleadius. The sagittal geometry was kept constant for all tests, withontact occurring only on the 21.55 mm radius during simulatedait. Idealized tibial insert geometry was constructed using a sag-ttal and coronal profile each with a different single radius. Con-ormity in each plane was defined as the femoral radius divided byhe tibial radius �15�, with all conformity changes created byhanging the tibial geometry.

Phase one tests utilized a matrix of sagittal and coronal confor-ities to blanket a broad design space representative of contem-

orary knee replacement geometries. The matrix consisted ofhree femoral coronal radii �20, 40, and 80 mm�, six combinationsf coronal and sagittal conformity varied separately on the medialide, and two combinations of coronal and sagittal conformityaried together on the lateral side �Table 1�. A wider range ofonditions was modeled on the medial side than on the lateral sideo keep the phase one test matrix to a reasonable size.

Phase two tests involved detailed analysis of the conformityonditions in phase one to which predicted wear volume was sen-itive. All phase two sensitivity tests were variations away from aominal case utilizing sagittal and coronal conformity of 0.5 inoth compartments and the intermediate femoral component coro-al radius of 40 mm. Starting from this nominal case, sagittalonformity was increased and decreased incrementally in the me-ial and lateral compartments separately and together �Table 2�,ith no changes made to coronal conformity. In addition, coronal

onformity was increased and decreased in both compartmentsogether without varying sagittal conformity to confirm the lack ofensitivity to geometry variations in this plane �Table 3�.

ResultsFor the phase one tests, sagittal but not coronal conformity

ignificantly affected predicted wear volume �Figs. 3 and 4�.hen lateral compartment coronal and sagittal conformity were 0,ear volume exhibited little change as medial compartment sag-

ttal conformity increased from 0 to 0.91 �Fig. 3�. In contrast,hen lateral compartment coronal and sagittal conformity were

Anterior

Lateral Medial 0

0.1

0.2

0.3

0.4

ig. 2 Wear scars and depths „in mm… predicted by the com-utational model for the implant geometry and simulationhown in Fig. 1

.5, wear volume decreased as medial compartment sagittal con-

ournal of Biomechanical Engineering

formity increased from 0 �i.e., flat� to 0.91 �i.e., high conformity�.However, the decrease from 0 to 0.5 �i.e., moderate conformity�was much larger than that from 0.5 to 0.91 �Fig. 4�. Regardless ofthe values of medial and lateral sagittal conformity, changing me-dial coronal conformity from 0 to 0.5 had little impact on pre-dicted wear volume. Changing the femoral component coronalradius from 20 mm to 80 mm also had little impact.

For the phase two tests, changes in sagittal conformity in one orboth compartments resulted in nonlinear changes in wear volume�Figs. 5–7�. When sagittal conformity was changed in either com-partment from its nominal value of 0.5, large increases in wearvolume occurred as sagittal conformity decreased toward 0 �i.e.,less conformal�, while only small decreases occurred when it in-creased toward 0.75 �i.e., more conformal�. When only medialsagittal conformity was changed, little change in lateral compart-ment wear volume occurred �Fig. 5�. A similar situation occurredwhen only lateral sagittal conformity was changed and medialsagittal conformity was held constant �Fig. 6�. The largest wearvolume changes occurred when sagittal conformity was varied inboth compartments together �Fig. 7�. Changes in coronal confor-mity in both compartments together resulted in little change inwear volume.

4 DiscussionThis study used a validated computational wear model to inves-

tigate the influence of sagittal and coronal conformity on wearvolume in an idealized total knee replacement design. The designwas representative of the features present in contemporary kneedesigns and was tested in a computational model of a Stanmoreknee simulator machine. The tests were performed in two phases,where the first phase blanketed a wide variety of TKR sagittal andcoronal geometry combinations, while the second phase focusedon conformity conditions from the first phase to which wear vol-ume was found to be sensitive. Overall, wear volume was muchmore sensitive to sagittal than coronal conformity changes anddecreased nonlinearly with corresponding reductions in slidingmotion, consistent with our original hypothesis. This sensitivitywas evident only when the medial and lateral compartments had

Table 1 Matrix of 36 different combinations of medial and lat-eral coronal and sagittal conformities used for the phase onetests. Femoral component sagittal profile was constant for alltests. In either direction, conformity of 0 corresponds to a flattibial insert „nonconformal…, 0.50 to a ratio of radii of 2:1 „mod-erately conformal…, and 0.91 to a ratio of radii of 1.1:1 „highlyconformal….

Femoralcoronalradius�mm�

Medialcoronal

conformity

Medialsagittal

conformity Lateral conformity

20 0.0 0.00

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or coronal and sagittalconformity of 0.5

20 0.0 0.5020 0.0 0.9120 0.5 0.0020 0.5 0.5020 0.5 0.9140 0.0 0.0040 0.0 0.5040 0.0 0.9140 0.5 0.0040 0.5 0.5040 0.5 0.9180 0.0 0.0080 0.0 0.5080 0.0 0.9180 0.5 0.0080 0.5 0.5080 0.5 0.91

different sagittal conformities. Furthermore, at least moderate sag-

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ttal conformity was needed in both compartments to minimizeear volume. Though not completely unexpected, these findingsay be useful for improving the wear resistance of future TKR

eometric designs.The nonlinear relationship between sagittal conformity and

ear volume reflects an underlying linear relationship between APranslation range, IE rotation range, and wear volume. When sag-ttal conformity is changed, the relative kinematics between theemoral component and tibial insert change as well. The mostbvious changes are in the range of AP translation and IE rotation.o investigate the relationship between wear volume and theseinematic ranges, we performed a two-variable linear regressionnalysis in MATLAB �The Mathworks, Natick, MA�. We found thator each of the three phase two tests, the R2 value was 0.95 origher, indicating that these two kinematic ranges are excellentredictors of wear volume. This finding helps explain why at leastome sagittal conformity is needed in both compartments to reach

Table 2 Sagittal conformity combinations usethe nominal design was varied three ways:compartment only, and in both compartments

Femoral sagittal radius �mm� 21.55 21.55Tibial sagittal radius �mm� Infinite 172.40Conformity 0.0 0.125

able 3 Coronal conformity combinations used for the phasewo tests. Coronal conformity of the nominal design was variedn both compartments together.

emoral coronal radius �mm� 40.00 40.00 40.00 40.00ibial coronal radius �mm� Infinite 160.00 80.00 53.33onformity 0.0 0.25 0.50 0.75

0

10

20

30

40

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Wearvolume(mm3 )

Medial sagittal conformity

mcc = 0, fcr = 20mcc = 0.5, fcr = 20mcc = 0, fcr = 40mcc = 0.5, fcr = 40mcc = 0, fcr = 80mcc = 0.5, fcr = 80

ig. 3 Phase one tests: wear volume as a function of changesn medial sagittal conformity when coronal and sagittal confor-

ity on the lateral side are 0. In the legend, “mcc” indicates theedial coronal conformity, while “fcr” indicates the femoral

oronal radius in mm.

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

Wearvolume(mm3 )

Medial sagittal conformity

ig. 4 Phase one tests: wear volume as a function of changesn medial sagittal conformity when coronal and sagittal confor-

ity on the lateral side are 0.5. Lines are the same as in Fig. 3.

21007-4 / Vol. 132, FEBRUARY 2010

the “diminishing returns” portion of the phase two wear volumeversus sagittal conformity curves �Figs. 5–7�.

Our computational results are in contrast to a previous in vitrosimulator study that investigated the influence of sagittal confor-mity on wear volume �19�. In that study, wear volume was mea-sured for two TKR designs—an existing design and a modifiedversion in which the posterior sagittal radius of the tibial insertwas increased �i.e., the design became less conformal�. The au-thors found that experimentally measured wear volumes from the

or the phase two tests. Sagittal conformity ofthe medial compartment only, in the lateralgether.

.55 21.55 21.55 21.55 21.55 21.55

.88 86.20 68.96 57.47 43.00 28.73

.188 0.250 0.313 0.375 0.500 0.750

0

10

20

30

40Medial

Lateral

Total

0.0 0.2 0.4 0.6 0.8Wearvolume(mm3 )

Sagittal conformity

Fig. 5 Phase two tests: wear volume as a function of changesin sagittal conformity of the nominal design when medial sag-ittal conformity was varied and lateral sagittal conformity washeld constant.

0

10

20

30

40

0.0 0.2 0.4 0.6 0.8

Wearvolume(mm3 )

Sagittal conformity

Fig. 6 Phase two tests: wear volume as a function of changesin sagittal conformity of the nominal design when lateral sagit-tal conformity was varied and medial sagittal conformity washeld constant. Lines are the same as in Fig. 5.

0.0 0.2 0.4 0.6 0.80

10

20

30

40

Wearvolume(mm3 )

Sagittal conformity

Fig. 7 Phase two tests: wear volume as a function of changesin sagittal conformity of the nominal design when medial andlateral sagittal conformity were varied together. Lines are the

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wo designs were not statistically different. There are two possiblexplanations why these results differ from those of our study.irst, the in vitro study used a displacement-controlled simulatorachine with prescribed AP translation and IE rotation. For this

ituation, the linear regression relationship developed from ouromputational simulations �see above� would predict no change inear volume for the two insert designs. Second, the in vitro studyid not specify the tibiofemoral sagittal conformity for the twoesigns, and it is possible that both designs were in the diminish-ng returns portion of the sagittal conformity range.

Our predicted AP displacement ranges as a function of sagittalonformity compare favorably with experimental measurementsade on an actual Stanmore simulator machine �24�. That study

nvestigated how TKR geometric design influences the resultinginematics. To evaluate whether our computational predictionsere reasonable, we calculated AP displacement range and sagit-

al conformity for the designs used in that study and plotted themgainst predictions from our study. For sagittal conformitiesreater than 0.2, the agreement between our predicted AP dis-lacement range and that measured in Ref. �24� was excellent. Foragittal conformities below 0.2, our predicted AP displacementanges were higher than those measured in Ref. �25�, possibly dueo “bottoming out” of the spring bumpers in the physical simulator

achine.The computational approach used in our study to predict wear

olume changes as a function of conformity changes could bemplemented as part of the design process utilized by orthopedicmplant companies. Implant designers could generate a wideange of geometry variations for initial investigation, similar tour phase one study, to screen design variations under consider-tion. They could then use those results to determine the mostromising design parameters on which to focus for a more de-ailed investigation, similar to our phase two study. By followinghis process, implant designers could minimize the creation andesting of physical prototypes for designs that would likely exhibitoor wear performance. Once an optimal design was identified, ahysical prototype of this design could be tested in a knee simu-ator machine and the resulting wear volume compared with thatf a nominal design, thereby providing a means for experimentalalidation of the final proposed design.

If such a design approach was followed, it would be critical toerform the physical validation tests on the same type of simulatorachine as used in the computational study. In particular, when

tudying the effects of conformity on wear volume, a simulatorachine should be chosen for which AP translation and IE rota-

ion are load controlled rather than motion controlled. It wouldlso be critical to ensure that the motion and load outputs pro-uced by the simulator machine closely matched those of theomputational study. The effect of errors in motion and load out-uts on the measured wear volume could be estimated by per-orming a Monte Carlo analysis using recently reported “ultrafast”ontact modeling techniques that are capable of performing wearimulations in a matter of seconds rather than minutes �28,46�. Inhis way, whether or not the measured wear volume was consis-ent with the computational prediction could be assessed objec-ively.

Even though idealized geometries were used in this study, theytill provide valuable insight into the effect of sagittal and coronalonformity changes on wear volume. Retrieval studies have at-empted to analyze the effect of conformity on wear in retrievedibial inserts, but few studies have looked at explicit quantitativehanges in sagittal and coronal conformity �1,11,47�. The resultsrom the present study suggest that increased conformity can re-uce wear, something that has been suggested by previous studies1,10–13,15�. Several retrieval studies have shown that more con-ormal inserts tend to reduce wear �1,11�. However, quantitativeonclusions on exactly what type of conformity, and how much,re needed to decrease wear volume significantly are hard to draw

rom retrieval studies. The main reason is confounding factors

ournal of Biomechanical Engineering

such as unknown patient activity levels, differing UHMWPEmanufacturing techniques, and a lack of detailed informationabout the conformity of the retrieved implants. Finite element�FE� studies have shown that increased conformity can lead todecreased stresses if the components are properly aligned�14–16�. Though decreased contact stress has been linked to adecrease in wear rate �48�, the corresponding increase in contactarea subjected to sliding may result in little net change in wearvolume �18�. The present study supports that hypothesis for sag-ittal conformities greater than about 0.5.

Minimizing wear is not the only goal when developing TKRgeometric designs. Other factors such as interface stresses andlaxity are important as well. On the one hand, increased confor-mity appears to decrease mild wear in a nonlinear diminishingfashion, which is beneficial, while on the other hand, it increasesinterface stresses and decreases laxity, which may be detrimental�23�. A recent in vivo study using instrumented knee implantsdemonstrated that golf in particular requires high rotational laxity,making high conformity undesirable for this task �49�. Thus, thegeometric design recommendations arising from this study mustbe interpreted within the larger scope of potentially competingdesign goals, and the various trade-offs must be weighed carefullyby the orthopedic implant design engineer.

The results of our study should not be surprising given knowl-edge available from previous studies. A change in conformity re-sults in altered contact pressure, contact area, and kinematics�15,50,51�. Increased conformity has been reported to decreasecontact pressure �15,51�. Thus, one might expect wear volume todecrease with increased conformity in a similar manner. However,for fixed kinematics, a previous simulation study reported thatdecreasing the contact pressure by increasing the insert thicknessproduced no change in wear volume calculated using Archard’swear law �18�. The potential reduction in wear volume resultingfrom decreased contact pressure was cancelled by a correspondingincrease in contact area subjected to pressure and sliding. In thepresent study, contact pressure was decreased and contact areaincreased by increasing conformity rather than insert thickness.Consequently, conformity affected wear volume by changing APtranslation and IE rotation rather than by changing contact pres-sure. Since one would expect these two kinematic quantities todecrease nonlinearly as conformity is increased, it was reasonableto hypothesize that wear volume would follow a similar trend.Further investigation is required to understand more fully the re-lationship between the radii of the contacting geometries and theamount of translational and rotational constraint.

Our computational study possesses several limitations. Onelimitation was that wear volume predictions for 5�106 cycles ofsimulated gait were generated by extrapolating one-cycle wearresults for virgin geometry. Thus, the surface geometry of theinsert was not worn gradually by the model as in real life, sincesimulation of progressive surface wear is much more demandingcomputationally. However, two previous computational studies ofknee simulator machines have shown that wear volume predic-tions, but not wear depth and area predictions, are insensitive towhether or not the surface geometry is changed progressively overa sequence of simulations �29,31�. Predicted wear volume has alsobeen shown to be insensitive to whether the tibial insert is treatedas a linear or nonlinear elastic material and whether or not a creepmodel is included in the wear prediction process �29�. Thus,extrapolation of one-cycle wear volume results out to5�106 cycles appears to be appropriate for design purposes,since osteolysis is a function of wear volume rather than weardepth or area. In contrast, progressive wear simulation is neededwhen attempting to validate proposed damage models using ex-perimental measurements of damage volume, area, and depth.

Another limitation of our wear prediction methodology was theuse of a constant wear factor. The selected value of1�10−7 mm3 /N m was chosen as representative of the range of

−6

values reported in the literature �approximately 1�10 to

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�10−8 mm3 /N m �42–45��. Since wear volume in our model islinear function of the selected wear factor, increasing or decreas-

ng the wear factor would scale all of our wear volume results upr down proportionally. Though wear factors can increase withross shear �52�, we used a constant wear factor since cross shears generally minimal in TKR designs �53� and since a previousomputational study produced excellent agreement with experi-ental wear volume measurements using a constant wear factor

29�. In our computational simulations, the designs that rotated theost �i.e., the less conformal designs� had the worst wear vol-

mes. Causing the wear factor to increase as a function of crosshear would only increase wear volume further for these designsnd would not change our general conclusions.

A limitation of the contact model used in our wear simulationsas the omission of friction. Though friction and wear are related

o surface roughness, modeling of friction is not required to pro-uce accurate wear volume predictions �29�. Archard’s wear laws not dependent on the presence or omission of a friction model,s the wear factor accounts for the influence of surface roughnessn wear volume. Inclusion of a friction model in the contactodel would, however, reduce the predicted anterior-posterior

ranslation range slightly, thereby reducing predicted wear volumelightly as well. Nonetheless, wear simulations performed withoutriction have been shown to match experimental wear volumeeasurements closely �29,31�, suggesting that inclusion of fric-

ion in the contact model is not critical for predicting wear volumeccurately.

A final limitation was that wear simulations in this study wereerformed exclusively for gait. Though surface damage is alteredhen other tasks such as stair climbing are simulated as well �34�,se of gait simulations alone still provides a basis for evaluatingverall wear trends.

cknowledgmentThis study was funded by an NSF CBET CAREER award to

.J.F. and by a MAKO Surgical Corporation grant to S.A.B.

eferences�1� Benjamin, J., Szivek, J., Dersam, G., Persselin, S., and Johnson, R., 2001,

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